Quantum Field Theory in de Sitter Space

Abstract

Usually elementary particle physics is based on the Poincaré group although the latter may be only the limiting form of the actual invariance group of the universe. One may have the feeling that cosmological changes of the space-time group will not change its microscopical consequences. On the other hand by contraction some important restrictions may be lost: going from the Poincaré group to the Galilei group the TCP — theorem or the connection between spin and statistics are lost. These restrictions are important even when apparently no relativistic velocities are involved. Similarly the difference between the Poincaré group and the de Sitter group could show up in laboratory experiments. Consequently we shall investigate how quantum field theory works for systems invariant under the de Sitter group. We do not mean to imply that we consider as established that we live in a de Sitter space but rather consider two different models of space-time, both invariant under the de Sitter group, as interesting possible representations of our cosmos.